


'''simple docstring'''


def      snake_case_  (    SCREAMING_SNAKE_CASE__ = 6008_5147_5143	):







				"""simple docstring"""





				try:
								_SCREAMING_SNAKE_CASE					:			List[str]							= int(SCREAMING_SNAKE_CASE__	)
				except (TypeError, ValueError):
								raise TypeError("""Parameter n must be int or castable to int."""	)
				if n <= 0:
								raise ValueError("""Parameter n must be greater than or equal to one."""	)
				_SCREAMING_SNAKE_CASE					:			str							= 1
				_SCREAMING_SNAKE_CASE					:			str							= 2
				while i * i <= n:
								while n % i == 0:
												_SCREAMING_SNAKE_CASE					:			List[Any]							= i
												n //= i
								i += 1
				if n > 1:
								_SCREAMING_SNAKE_CASE					:			Optional[Any]							= n
				return int(SCREAMING_SNAKE_CASE__	)


if __name__ == "__main__":
				print(F"{solution() = }")








'''simple docstring'''


import math







def      snake_case_  (    SCREAMING_SNAKE_CASE__	):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE					:			Tuple							= math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

				return exponent == int(SCREAMING_SNAKE_CASE__	)







def      snake_case_  (    SCREAMING_SNAKE_CASE__ = 1 / 1_2345	):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE					:			str							= 0
				_SCREAMING_SNAKE_CASE					:			str							= 0

				_SCREAMING_SNAKE_CASE					:			int							= 3
				while True:
								_SCREAMING_SNAKE_CASE					:			Optional[int]							= (integer**2 - 1) / 4
								# if candidate is an integer, then there is a partition for k
								if partition_candidate == int(SCREAMING_SNAKE_CASE__	):
												_SCREAMING_SNAKE_CASE					:			int							= int(SCREAMING_SNAKE_CASE__	)
												total_partitions += 1
												if check_partition_perfect(SCREAMING_SNAKE_CASE__	):
																perfect_partitions += 1
								if perfect_partitions > 0:
												if perfect_partitions / total_partitions < max_proportion:
																return int(SCREAMING_SNAKE_CASE__	)
								integer += 1


if __name__ == "__main__":
				print(F"{solution() = }")




